Which of the following numbers is a multiple of 11? ${45,66,74,84,114}$
Solution: The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $45 \div 11 = 4\text{ R }1$ $66 \div 11 = 6$ $74 \div 11 = 6\text{ R }8$ $84 \div 11 = 7\text{ R }7$ $114 \div 11 = 10\text{ R }4$ The only answer choice that leaves no remainder after the division is $66$ $ 6$ $11$ $66$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $66$ $66 = 2\times3\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $66$. We can say that $66$ is divisible by $11$.